Skip to main content
Physics LibreTexts

2.4: Convergence

  • Page ID
    7076
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Figure II.5 shows a lens made of glass of refractive index 1.50. To the left of the lens is air (refractive index 1.00). To the right of the lens is water (refractive index 1.33). A converging beam of light is incident upon the lens directed toward a virtual object O that is 60 cm from the lens. After refraction through the lens, the light converges to a real image I that is 20 cm from the lens.

    Screen Shot 2017-07-14 at 9.25.27 AM.png

    I am not at this stage going to ask you to calculate the radii of curvature of the lens. (You can’t – you need one more item of information.) I just want to use this diagram to define what I mean by convergence.

    The convergence of the light at the moment when it is incident upon the lens is called the initial convergence \(C_1\), and it is defined as follows:

    \[ initial\space convergence = \frac{Refractive\space index}{Object \, distance}. \label{eq:2.4.1} \]

    The convergence of the light at the moment when it leaves the lens is called the final convergence \(C_2\), and it is defined as follows:

    \[ final\space convergence = \frac{Refractive\space index}{Image \, distance}. \label{eq:2.4.2} \]

    Sign convention

    • Converging light has positive convergence;
    • Diverging light has negative convergence.

    Example \(\PageIndex{1}\)

    Initial convergence = \(+ \frac{1.00}{60}=+0.01667\) cm-1.

    Final convergence = \(+ \frac{1.33}{20}=+0.06650\) cm-1.

    Notice that, before the light enters the lens, it is in a medium of refractive index 1.00. Thus the relevant refractive index is 1.00, even though the virtual object is in the water.


    This page titled 2.4: Convergence is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

    • Was this article helpful?